Colloquiums & Seminars 2003-2004
back to Seminars and Colloquiums 2006
Colloquium, Thursday, December 9, 2004 @ 2.30 pm
Dr Carl Ras, University of Johannesburg
"Classifying trees labeled with a condition at distance two"
Abstract. An L(j, k)-labeling of a graph G, where j \ge k, is defined as a function f : V (G) \mapsto Z^+U {0} such that for any two vertices u, v \in V (G) if uv \in E(G) then |f(u) − f(v)| \ge j and if d(u, v) = 2 then |f(u) − f(v)| \ge k. The largest label used by f is called the span of f. The smallest span amongst all L(j, k)-labelings of G is the L(j, k)-number of G and is denoted by \lambda_{j,k}(G). An L(j, k)-labeling of G that has a span of j,k(G) is called a span labeling of G. We consider L(2, 1)-labelings. For a given tree T we always have \Delta(T) + 1 \le \lambda_{2,1}(T) \le \Delta(T) + 2. We characterise those trees T for which \lambda_{2,1}(T) = \Delta(T) + 1.
Colloquium, Friday November 19, 2004 @ 11.00 am
Dr. Lincoln Liu, University of South Carolina
"Guessing Secrets"
Abstract. Suppose we are given some fixed (but unknown) subset X of a set W = F_2^n, where F_2 denotes the field of two elements. We would like to learn as much as possible about the elements of X by asking certain binary questions. Each ``question" Q is some element of W, and the ``answer" to Q is just the inner product Q · (in F_2) for some x in Î X. However, the choice of x is made by a truthful (but possibly malevolent) adversary A, whom we may assume is trying to choose answers so as to yield as little information as possible about X. In this paper, we study various aspects of this problem. In particular, we are interested in extracting as much information as possible about X from \AA's answers. Although \AA can prevent us from learning the identity of any particular element of X, with appropriate questions we can still learn a lot about X. We determine the maximum amount of information that can be recovered and discuss the optimal strategies for selecting questions. For the case that |X|=2, we give an O(n^3) algorithm for an optimal strategy. However, for the case that |X| >=3, we show that no such polynomial-time algorithm can exist, unless P = NP.
This is a joint work with Fan Chung Graham and Ronald Graham.
Statistical Colloquium, Friday November 19, 2004 @ 2.30 pm
Dr. Justine Shults, Department of Biostatistics and Epidemiology,
School of Medicine, University of Pennsylvania
"Analysis of Repeated Bouts of Measurements in the Framework of Generalized Estimating Equations"
Abstract. We consider a longitudinal study of Interstitial Cystitis (IC) in women in which the time between bouts of repeated measurements is large relative to the within bout separation in time. Our outcome of interest is the number of nocturnal voids that we model via quasi-least squares (QLS) in the framework of generalized estimating equations
(GEE). To account for potential intra-subject correlation we directly apply a correlation structure that previously was only implemented in an ad-hoc approach using GEE. We describe this structure and results of our analysis. We then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler
structure can prevent substantial losses in efficiency in estimation of the regression parameter. These comparisons involve the limiting values of the estimates of the correlation parameters, which are not consistent for the misspecification scenarios considered here. In addition, we compare QLS versus GEE when the structure is misspecified as equicorrelated. For the examples we consider, the losses in efficiency are similar, but slightly smaller for GEE.
This is joint work with Carissa A. Mazurick and Richard Landis.
Analysis Seminar, Wednesday, November 17, 2004 @ 10:30, Room 796
Dr. Patyi, Math & Stat
"Irrationality and transcendence"
Abstract. In this expository talk on analytic number theory we will look at a classical result of Gelfond and Schneider that shows in particular that the Euler number (e) and (pi) are irrational, moreover, they are not roots of polynomials with rational coefficients. We will follow Appendix 1 of the book "Algebra" by Serge Lang. The proof involves some simple linear algebra and some estimates of growth rates for certain functions of finite order. The talk will be accessible to all with the rudiments of linear algebra, and of functions of one complex variable.
Statistical Colloquium, Friday, November 12, 2004 @ 2:00 pm (Refreshments 1:45 p.m.)
Dr. Xiangrong Yin
Department of Statistics, University of Georgia.
"On estimation for dual central subspaces in dimension reduction"
Abstract. Recently developed dimension reduction methods focus on predictors in regression, even with multivariate response. In this paper, we extend the dimension reduction ideas of regression to both sets of variables, responses and predictors. A new concept, dual central subspace (DCS), is introduced. We propose new methods for
identifying and estimating the DCS. Existing methods are also discussed for their advantages and disadvantages. Examples are presented for illustration.
This is a joint work with Lixing Zhu.
11/10/04 @ 10:30, Room 796
Dr. Smirnova, Math & Stat
"Inverse Problem in Optical Tomography and its Numerical Investigation by Iteratively Regularized Methods"
Colloquium, Friday, October 29, 2004 @ 2:30 p.m. (Refreshments @ 2:00 p.m.)
Dr. Anuradha Roy
Department of Management Science and Statistics
University of Texas at San Antonio
Abstract. The problem of classification of doubly multivariate measurements i.e. multiple-response, repeated measurements arises in many diverse areas such as bio-medical, psychological, pharmaceutical and epidemiological research. Traditional
classification rules cannot be applied as the number of variables becomes exceedingly large. New classification rules are developed by incorporating some correlation structures on these data. We will see that in the classification problem, it is extremely important to consider the correct correlation structure on the repeated measures. Assumption of incorrect structure leads to higher misclassification error rate. We will present the
results on a real data set from medical science as well as on a simulated data set.
10/20/04 @ 10:30, Room 796
Dr. Bakonyi , Math & Stat
"Positive definite functions on groups"
10/13/04 @ 10:30, Room 796
Dr. Livingstone, Math & Stat
"Poisson Summation Formula and Riemann Integral"
Abstract. Classical Poisson summation formula says that the summation of a
suitable real function at integer points can be computed by summing up
its Fourier transform at integer points. Poisson summation formula plays
an important role in analytic number theory. In this talk I will give an
introduction to this topic and use it to estimate Riemann integral.I
will also mention some open problems. Only the basic knowledge about
Fourier transform is required.
09/22, 09/92/04 and 10/06/04
@ 10:30, Room 796
Dr. Patyi, Math & Stat
"Shannon's problem on the monotonicity of entropy".
All (graduate students, faculty and visitors) are welcome.
Abstract. In this talk, probably in two parts, we will most probably discuss probability, namely, after some preliminaries we will look at a recent paper by Artstein, Ball, Barthe and Naor (to appear in the Journal of the American Mathematical Society) that completely solves the titular problem, which is a classical one related to information theory. Most parts of the talk will be accessible to mathematicians and statisticians, experienced and inexperienced alike.
09/24/04 @ 13:00
Gennady S Cymbalyuk from Physics and Astronomy, GSU
"Bifurcation Analysis of Neuronal Rhythmogenesis"
Abstract. The bursting activity of neurons has been shown to be important for different functions of the central nervous system, especially for the control of rhythmic movements Various patterns of bursting activities have been described in terms of the qualitative theory of slow-fast systems. However, the classification of routes describing possible transitions between tonic spiking and bursting activities is yet incomplete and remains a fundamental problem for both neuroscience and the theory of dynamical systems We discuss two new mechanisms of continuous transitions between tonic spiking and bursting regimes in neuron models following Hodgkin-Huxley formalism. Both transitions are based on homoclinic saddle-node bifurcations of orbits of codimension. We yield universal estimates for duration of bursting activities as a control parameter varies. Both transitions are reversible as the parameter is changed backward. These features describe a biophysically plausible control mechanism for regulation of bursting activity. In this work we have employed the technique of Pontryagin's averaging and made it easy to comprehend in the computational neuroscience context.
This work is done in collaboration with Ron Calabrese (Emory) and Andrey Shilnikov
(GSU) .
09/24/04 @ 2.30pm
Mark Borodovsky
Schools of Biology and Biomedical Engineering, Georgia Tech
Abstract. I will focus on "informatics" part of Bioinformatics which deals with genetic information stored in DNA and actualized in proteins and cell machines. This overview type talk will draw parallels with notions, models and algorithms of information processing in other evolving systems such as means of human communication.
The Department of Mathematics and Statistics presents…
A Mandatory Event, Departmental Workshop Day Presentation:
So What Does That Grade of A Mean? Developing Uniform Assessment Procedures
Friday, August 20, 9:00 am – 4:00 pm, Georgia State University Campus
Food provided & Cocktail Fellowship Reception for you and a guest @ 5:30 pm
The Department of Mathematics & Statistics
Georgia State University, 404.651.2253
Colloquium
Title: Inverse Problem in Optical Tomography
Speaker: Dr. Taufiquar Khan
Department of Mathematical Sciences - Clemson University
Date: Friday, November 21, 2003
Time: 2:00 (Refreshment will be served at 1:45)
Place: 796 College of Education
* * * *
Abstract
Optical tomography (OT), as a potential medical imaging modality, has been investigated for more than a decade. The idea of OT is the reconstruction of the spatial distribution of optical properties within tissue by use of measurements of near-infrared light along the tissue boundary. Light propagation within tissue is generally described by the radiative transfer equation (RTE). In this talk, a general overview of the inverse problem associated with the reconstruction of the spatial distribution of optical properties in OT via optimization, will be given. The practical issues of reconstruction via optimization including regularization, uniqueness, and stability of the inverse problem will be discussed. Some of the open questions and challenges will also be presented.
Colloquium
Title: Recent Results in Total Domination in Graphs
Speaker: Michael Henning
School of Mathematics, Statistics & Information Technology - University of Natal
Pietermaritzburg, South Africa
Date: Tuesday, December 2, 2003
Time: 2:00 (Refreshment will be served at 1:45)
Place: 796 College of Education
* * * *
Abstract
A set S of vertices in a graph G without isolated vertices is a total dominating set of G if every vertex of G is adjacent to a vertex in S. The total domination number ofG is the minimum cardinality of a total dominating set in G. In this talk, we discuss recent results on total domination in graphs.
Seminars
Image Analysis Seminar
Every other Wednesday, 12:30 - 1:30 in 796 COE.
Next presentation: 19 February 2003
* * * *
Bioinformatics
* * * *
Analysis Seminar
Our seminar will be on Wednesdays from 11:00-12:00 in 796 COE.
Wednesday, January 15:
Speaker: Alexandra Smirnova
Title: 'Regularized Quasi-Newton methods for unstable operator equations'
Wednesday, January 22:
Speaker: Mihai Bakonyi
Title: To be announced
Wednesday, January 29:
Speaker: Andrey Shilnikov
Title: Smale horseshoes in endomorphisms and chaos in discrete neuron models